1. TIVDM2Functional Programming Language Concepts 1 Concepts from Functional Programming Languages Peter Gorm Larsen

2. TIVDM2Functional Programming Language Concepts 2 Agenda  Introduction to the Functional Programming Paradigm The notion of higher order functions Polymorphic examples of standard higher order functions

3. TIVDM2Functional Programming Language Concepts 3 Introduction to FP The design of the imperative languages is based directly on the von Neumann architecture Efficiency is the primary concern, rather than the suitability of the language for software development The design of the functional languages is based on mathematical functions A solid theoretical basis that is also closer to the user, but relatively unconcerned with the architecture of the machines on which programs will run

4. TIVDM2Functional Programming Language Concepts 4 Principles of FP Treats computation as evaluation of mathematical functions (and avoids state) Data and programs are represented in the same way Functions as first-class values – Higher-order functions: functions that operate on, or create, other functions – Functions as components of data structures Lambda calculus provides a theoretical framework for describing functions and their evaluation It is a mathematical abstraction rather than an imperative programming language

5. TIVDM2Functional Programming Language Concepts 5 History lambda calculus (Church, 1932) simply typed lambda calculus (Church, 1940) lambda calculus as prog. lang. (McCarthy(?), 1960, Landin 1965) polymorphic types (Girard, Reynolds, early 70s) algebraic types ( Burstall & Landin, 1969) type inference (Hindley, 1969, Milner, mid 70s) lazy evaluation (Wadsworth, early 70s) Equational definitions Miranda 80s Type classes Haskell 1990s Microsoft F# etc 2000s

6. TIVDM2Functional Programming Language Concepts 6 Varieties of FP languages Typed (ML, Haskell) vs untyped (Scheme, Erlang) Pure vs Impure impure have state and imperative features pure have no side effects, “referential transparency” Strict vs Lazy evaluation

7. TIVDM2Functional Programming Language Concepts 7 Declarative style of programming Declarative Style of programming - emphasis is placed on describing what a program should do rather than prescribing how it should do it. Functional programming - good illustration of the declarative style of programming. A program is viewed as a function from input to output. Logic programming – another paradigm A program is viewed as a collection of logical rules and facts (a knowledge-based system). Using logical reasoning, the computer system can derive new facts from existing ones.

8. TIVDM2Functional Programming Language Concepts 8 Functional style of programming A computing system is viewed as a function which takes input and delivers output. The function transforms the input into output. Functions are the basic building blocks from which programs are constructed. The definition of each function specifies what the function does. It describes the relationship between the input and the output of the function.

9. TIVDM2Functional Programming Language Concepts 9 Agenda Introduction to the Functional Programming Paradigm  The notion of higher order functions Polymorphic examples of standard higher order functions

10. TIVDM2Functional Programming Language Concepts 10 First-Class Functions Data values are first-class if they can be assigned to local variables be components of data structures be passed as arguments to functions be returned from functions be created at run-time

11. TIVDM2Functional Programming Language Concepts 11 Higher-order Functions Every function has an order: A function that does not take any functions as parameters, and does not return a function value, has order 1 A function that takes a function as a parameter or returns a function value has order n+1, where n is the order of its highest-order parameter or returned value A small example: Twice: (int -> int) * int -> int Twice(f,x) == f( f (x)) Or TwiceCur: (int -> int)-> int -> int TwiceCur(f)(x) == f( f (x))

12. TIVDM2Functional Programming Language Concepts 12 Functions in Programming Languages How functions are treated by programming languages? Languagepassed as arguments returned from functions nested scope JavaNo CYes No C++Yes No PascalYesNoYes Modula-3YesNoYes SchemeYes MLYes

13. TIVDM2Functional Programming Language Concepts 13 Nested Functions and Closures Return a function from function call function f(x) { var y = x; return function (z){y += z; return y;} } var h = f(5); h(3); In order to handle this one needs to introduce closures A closure is a function that captures the bindings of free variables in its lexical context.

14. TIVDM2Functional Programming Language Concepts 14 Agenda Introduction to the Functional Programming Paradigm The notion of higher order functions  Polymorphic examples of standard higher order functions

15. TIVDM2Functional Programming Language Concepts 15 Predefined Higher-Order Functions in Functional Languages We will use three important predefined higher-order functions: map filter foldr foldl Actually, foldr and foldl are very similar, as you might guess from the names

16. TIVDM2Functional Programming Language Concepts 16 The Map Function Map applies a function to every element of a list: Map[@A,@B]: (@A -> @B) -> seq of @A -> seq of @B Map(f)(list) == [f(list(i)) | i in set inds list]

17. TIVDM2Functional Programming Language Concepts 17 The Filter Function Filter selects every element that satisfies a predicate: Filter[@A]: (@A -> bool) -> seq of @A -> seq of @A Filter(pred)(list) == [list(i) | i in set inds list & pred(list(i))]

18. TIVDM2Functional Programming Language Concepts 18 The FoldR Function Folds all elements in a list from the right into one value (a simple pattern of recursion): FoldR[@A,@B]: (@A * @B -> @B) -> @B -> seq of @A -> @B FoldR(f)(neutral)(list) == if list = [] then neutral else f(hd list,FoldR(f)(neutral)(tl list)) Example usage: Sum = FoldR(+)(0) Product = FoldR(*)(1) Or = FoldR(or)(false) And = FoldR(and)(true)

19. TIVDM2Functional Programming Language Concepts 19 Summary What have I presented today? Introduction to the Functional Programming Paradigm The notion of higher order functions Polymorphic examples of standard higher order functions What do you need to do now? Complete your distributed real time model for your project

20. TIVDM2Functional Programming Language Concepts 20 Quote of the day Program designers have a tendency to think of the users as idiots who need to be controlled. They should rather think of their program as a servant, whose master, the user, should be able to control it. If designers and programmers think about the apparent mental qualities that their programs will have, they'll create programs that are easier and pleasanter — more humane — to deal with. John McCarthy